Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 11/2012, Volume 17, Issue 11, pp. 4097 - 4103

► A new approach based on the homotopy analysis method is adopted for the Thomas–Fermi equation. ► Fast convergence and better accuracy is obtained by...

Thomas–Fermi equation | Computational cost | Analytic solution | Padé approximant | Homotopy analysis method | Thomas-Fermi equation | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | 2-DIMENSIONAL VISCOUS-FLOW | APPROXIMATE SOLUTION | PHYSICS, MATHEMATICAL | Pade approximant

Thomas–Fermi equation | Computational cost | Analytic solution | Padé approximant | Homotopy analysis method | Thomas-Fermi equation | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | 2-DIMENSIONAL VISCOUS-FLOW | APPROXIMATE SOLUTION | PHYSICS, MATHEMATICAL | Pade approximant

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2008, Volume 212, Issue 2, pp. 231 - 244

In this paper, an iterative method is constructed to solve the linear matrix equation AXB = C over skew-symmetric matrix X. By the iterative method, the...

Skew-symmetric solution | Iterative method | Least-norm skew-symmetric solution | Optimal approximate solution

Skew-symmetric solution | Iterative method | Least-norm skew-symmetric solution | Optimal approximate solution

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 05/2015, Volume 102, Issue 5, pp. 966 - 990

SummaryOne of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of...

model reduction | approximate Bayesian inference | inverse problem | adaptive Markov chain Monte Carlo | DISCRETE EMPIRICAL INTERPOLATION | BASES | MONTE-CARLO METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | SYSTEMS | PROPER ORTHOGONAL DECOMPOSITION | PARAMETER | Monte Carlo method | Models | Inverse problems | Partial differential equations | Mathematical models | Model reduction | Computational efficiency | Sampling | Bayesian analysis | Standards | Construction costs | MATHEMATICS AND COMPUTING

model reduction | approximate Bayesian inference | inverse problem | adaptive Markov chain Monte Carlo | DISCRETE EMPIRICAL INTERPOLATION | BASES | MONTE-CARLO METHODS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | DYNAMICS | SYSTEMS | PROPER ORTHOGONAL DECOMPOSITION | PARAMETER | Monte Carlo method | Models | Inverse problems | Partial differential equations | Mathematical models | Model reduction | Computational efficiency | Sampling | Bayesian analysis | Standards | Construction costs | MATHEMATICS AND COMPUTING

Journal Article

Energy Conversion and Management, ISSN 0196-8904, 12/2015, Volume 106, pp. 543 - 556

•A novel optimal carbon-energy combined-flow (OCECF) model is firstly established.•A novel approximate ideal multi-objective solution Q(λ) learning is...

Multi-objective optimization | Optimal carbon-energy combined-flow | Stochastic optimal weights | Approximate ideal multi-objective solution Q(λ) | Q(lambda) | UNIT COMMITMENT | DISPATCH | ENERGY & FUELS | PHYSICS, NUCLEAR | BEE COLONY ALGORITHM | PARTICLE SWARM OPTIMIZATION | MECHANICS | THERMODYNAMICS | Approximate ideal multi-objective solution | GRAVITATIONAL SEARCH ALGORITHM | GENERATION | CAPTURE | Electric power systems | Algorithms | Learning | Policies | Approximation | Dynamics | Deviation | Carbon | Dynamical systems | Optimization

Multi-objective optimization | Optimal carbon-energy combined-flow | Stochastic optimal weights | Approximate ideal multi-objective solution Q(λ) | Q(lambda) | UNIT COMMITMENT | DISPATCH | ENERGY & FUELS | PHYSICS, NUCLEAR | BEE COLONY ALGORITHM | PARTICLE SWARM OPTIMIZATION | MECHANICS | THERMODYNAMICS | Approximate ideal multi-objective solution | GRAVITATIONAL SEARCH ALGORITHM | GENERATION | CAPTURE | Electric power systems | Algorithms | Learning | Policies | Approximation | Dynamics | Deviation | Carbon | Dynamical systems | Optimization

Journal Article

ACM Computing Surveys (CSUR), ISSN 0360-0300, 05/2019, Volume 52, Issue 2, pp. 1 - 38

Complexity and variety of modern multiobjective optimisation problems result in the emergence of numerous search techniques, from traditional mathematical...

indicator | metaheuristic | multi-criteria optimisation | measure | metric | evolutionary algorithms | exact method | heuristic | performance assessment | Quality evaluation | multobjective optimisation | Multi-criteria optimisation | Multobjective optimisation | Metaheuristic | Performance assessment | Exact method | Measure | Metric | Evolutionary algorithms | Indicator | Heuristic | APPROXIMATE SOLUTION SETS | MANY-OBJECTIVE OPTIMIZATION | LOCAL SEARCH | HYPERVOLUME INDICATOR | GENETIC ALGORITHM | PERFORMANCE METRICS | CONVERGENCE | COMPUTER SCIENCE, THEORY & METHODS | SELECTION | PARETO FRONTIER | Multiple objective analysis | Quality assessment | Indicators | Quality | Optimization | Mathematical programming

indicator | metaheuristic | multi-criteria optimisation | measure | metric | evolutionary algorithms | exact method | heuristic | performance assessment | Quality evaluation | multobjective optimisation | Multi-criteria optimisation | Multobjective optimisation | Metaheuristic | Performance assessment | Exact method | Measure | Metric | Evolutionary algorithms | Indicator | Heuristic | APPROXIMATE SOLUTION SETS | MANY-OBJECTIVE OPTIMIZATION | LOCAL SEARCH | HYPERVOLUME INDICATOR | GENETIC ALGORITHM | PERFORMANCE METRICS | CONVERGENCE | COMPUTER SCIENCE, THEORY & METHODS | SELECTION | PARETO FRONTIER | Multiple objective analysis | Quality assessment | Indicators | Quality | Optimization | Mathematical programming

Journal Article

Journal of Hydrology, ISSN 0022-1694, 09/2017, Volume 552, pp. 544 - 553

•Improved approximate solution for dynamic erosion to describe first flush effect.•The solution converges to the steady state solution in the long run.•Average...

GUEST | Dynamic soil erosion processes | Overland flow | Approximate solution | SEDIMENT TRANSPORT | SHEET FLOW | EQUATIONS | 1ST FLUSH | WATER RESOURCES | WATER EROSION | MODEL | HIGHWAY RUNOFF | ENGINEERING, CIVIL | GEOSCIENCES, MULTIDISCIPLINARY | OVERLAND-FLOW | SOIL-EROSION | RAINFALL IMPACT | Runoff | Sediments (Geology) | Soil erosion

GUEST | Dynamic soil erosion processes | Overland flow | Approximate solution | SEDIMENT TRANSPORT | SHEET FLOW | EQUATIONS | 1ST FLUSH | WATER RESOURCES | WATER EROSION | MODEL | HIGHWAY RUNOFF | ENGINEERING, CIVIL | GEOSCIENCES, MULTIDISCIPLINARY | OVERLAND-FLOW | SOIL-EROSION | RAINFALL IMPACT | Runoff | Sediments (Geology) | Soil erosion

Journal Article

Physics Reports, ISSN 0370-1573, 04/2013, Volume 525, Issue 1, pp. 1 - 166

The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models....

Statistical interpretation | Reduction | Quantum measurement problem | Ideal and imperfect measurements | Registration | Decoherence | Pointer | Apparatus | Dynamical models | Collapse of the wavefunction | Truncation | FOKKER-PLANCK EQUATION | BROWNIAN-MOTION | PHYSICS, MULTIDISCIPLINARY | DECOHERENT HISTORIES | APPROXIMATE MEASUREMENT | EXACTLY SOLVABLE MODEL | YIELD CONTRARY INFERENCES | INCOMPLETE DESCRIPTIONS | CLASSICAL DYNAMICS | EXPERIMENTAL VIOLATION | BELLS-INEQUALITY | Measurement | Ferromagnetism | Magnetization | Quantum theory

Statistical interpretation | Reduction | Quantum measurement problem | Ideal and imperfect measurements | Registration | Decoherence | Pointer | Apparatus | Dynamical models | Collapse of the wavefunction | Truncation | FOKKER-PLANCK EQUATION | BROWNIAN-MOTION | PHYSICS, MULTIDISCIPLINARY | DECOHERENT HISTORIES | APPROXIMATE MEASUREMENT | EXACTLY SOLVABLE MODEL | YIELD CONTRARY INFERENCES | INCOMPLETE DESCRIPTIONS | CLASSICAL DYNAMICS | EXPERIMENTAL VIOLATION | BELLS-INEQUALITY | Measurement | Ferromagnetism | Magnetization | Quantum theory

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 04/2019, Volume 96, Issue 4, pp. 729 - 752

Let ( ), let with closed range. In this paper, utilizing the gap between closed subspaces and the perturbation bounds of metric projections, we present some...

Primary: 47A05 | Metric generalized inverse | Secondary: 46B20 | perturbation | best approximate solution | Subspaces | Generalized inverse | Ill-posed problems (mathematics)

Primary: 47A05 | Metric generalized inverse | Secondary: 46B20 | perturbation | best approximate solution | Subspaces | Generalized inverse | Ill-posed problems (mathematics)

Journal Article

9.
Full Text
Online solution of nonlinear two‐player zero‐sum games using synchronous policy iteration

International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 09/2012, Volume 22, Issue 13, pp. 1460 - 1483

SUMMARY The two‐player zero‐sum (ZS) game problem provides the solution to the bounded L2‐gain problem and so is important for robust control. However, its...

Nash equilibrium | approximate dynamic programming | Hamilton–Jacobi–Isaacs equation | synchronous zero‐sum game policy iteration | Hamilton-Jacobi-Isaacs equation | synchronous zero-sum game policy iteration | H-INFINITY CONTROL | MATHEMATICS, APPLIED | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Neural networks | Algorithms

Nash equilibrium | approximate dynamic programming | Hamilton–Jacobi–Isaacs equation | synchronous zero‐sum game policy iteration | Hamilton-Jacobi-Isaacs equation | synchronous zero-sum game policy iteration | H-INFINITY CONTROL | MATHEMATICS, APPLIED | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Neural networks | Algorithms

Journal Article

Information Sciences, ISSN 0020-0255, 12/2017, Volume 418-419, pp. 184 - 185

Gong et al. (Information Sciences 266 (2014) 112–133) proposed a method of solving dual fuzzy matrix equations. The aim of this note is to make the researchers...

Fuzzy numbers | Dual fuzzy matrix equations | Fuzzy approximate solutions | COMPUTER SCIENCE, INFORMATION SYSTEMS

Fuzzy numbers | Dual fuzzy matrix equations | Fuzzy approximate solutions | COMPUTER SCIENCE, INFORMATION SYSTEMS

Journal Article

Physics Letters A, ISSN 0375-9601, 2001, Volume 285, Issue 5, pp. 355 - 362

Based upon the well-known Riccati equation, a new generalized transformation is presented and applied to solve Whitham–Broer–Kaup (WBK) equation in shallow...

Approximate equation for long water waves | Variant Boussinesq equation | Periodic wave solution | Riccati equation | Solitary wave solution | WBK equation | TRANSFORMATION | variant Boussinesq equation | MATHEMATICAL PHYSICS | solitary wave solution | periodic wave solution | PHYSICS, MULTIDISCIPLINARY | approximate equation for long water waves | VARIANT BOUSSINESQ EQUATIONS

Approximate equation for long water waves | Variant Boussinesq equation | Periodic wave solution | Riccati equation | Solitary wave solution | WBK equation | TRANSFORMATION | variant Boussinesq equation | MATHEMATICAL PHYSICS | solitary wave solution | periodic wave solution | PHYSICS, MULTIDISCIPLINARY | approximate equation for long water waves | VARIANT BOUSSINESQ EQUATIONS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2006, Volume 177, Issue 2, pp. 488 - 494

The aim of the present analysis is to apply Adomian decomposition method for the solution of a time-fractional Navier–Stokes equation in a tube. By using an...

Navier–Stokes equations | Caputo fractional derivative | Decomposition method | Navier-Stokes equations | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | decomposition method | DIFFERENTIAL-EQUATIONS | CONVERGENCE | Fluid dynamics | Methods

Navier–Stokes equations | Caputo fractional derivative | Decomposition method | Navier-Stokes equations | APPROXIMATE SOLUTIONS | MATHEMATICS, APPLIED | decomposition method | DIFFERENTIAL-EQUATIONS | CONVERGENCE | Fluid dynamics | Methods

Journal Article

13.
Full Text
A bounded and monotone finite-difference solution of a hyperbolic Burgers–Fisher equation

International Journal of Modern Physics C, ISSN 0129-1831, 12/2018, Volume 29, Issue 12, p. 1850122

In this work, a nonlinear finite-difference scheme is provided to approximate the solutions of a hyperbolic generalization of the Burgers–Fisher equation from...

finite-difference method | Hyperbolic Burgers-Fisher equation | monotonicity | nonlinear discretization | positivity and boundedness | traveling-wave solutions | STOPPING TIME | EXPONENTIAL METHOD | MODEL | PHYSICS, MATHEMATICAL | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | APPROXIMATE | PRESERVING METHOD | WAVE-EQUATIONS

finite-difference method | Hyperbolic Burgers-Fisher equation | monotonicity | nonlinear discretization | positivity and boundedness | traveling-wave solutions | STOPPING TIME | EXPONENTIAL METHOD | MODEL | PHYSICS, MATHEMATICAL | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | APPROXIMATE | PRESERVING METHOD | WAVE-EQUATIONS

Journal Article

Composite Structures, ISSN 0263-8223, 01/2016, Volume 135, pp. 74 - 82

In this work an approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure is...

The Mori–Tanaka method | Approximate analytical solution | The Reuss method | The Voigt method | Functionally graded material | Thick-walled tube | The Mori-Tanaka method | MECHANICS | VESSELS | HOLLOW CYLINDERS | MATERIALS SCIENCE, COMPOSITES | ELASTIC ANALYSIS | STRESSES | Mechanical engineering | Methods

The Mori–Tanaka method | Approximate analytical solution | The Reuss method | The Voigt method | Functionally graded material | Thick-walled tube | The Mori-Tanaka method | MECHANICS | VESSELS | HOLLOW CYLINDERS | MATERIALS SCIENCE, COMPOSITES | ELASTIC ANALYSIS | STRESSES | Mechanical engineering | Methods

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2003, Volume 187, Issue 1, pp. 318 - 342

We study the numerical solution of the time-dependent Gross–Pitaevskii equation (GPE) describing a Bose–Einstein condensate (BEC) at zero or very low...

Approximate ground state solution | Gross–Pitaevskii equation | Bose–Einstein condensation (BEC) | Defocusing/focusing nonlinearity | Time-splitting spectral method | Bose-Einstein condensation (BEC) | Gross-Pitaevskii equation | VORTICES | GROUND-STATE | approximate ground state solution | time-splitting spectral method | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | COLLECTIVE EXCITATIONS | PHYSICS, MATHEMATICAL | TRAPPED NEUTRAL ATOMS | VORTEX | EXCITED-STATES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DILUTE GAS | defocusing/focusing nonlinearity | SEMICLASSICAL LIMIT | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Approximate ground state solution | Gross–Pitaevskii equation | Bose–Einstein condensation (BEC) | Defocusing/focusing nonlinearity | Time-splitting spectral method | Bose-Einstein condensation (BEC) | Gross-Pitaevskii equation | VORTICES | GROUND-STATE | approximate ground state solution | time-splitting spectral method | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | COLLECTIVE EXCITATIONS | PHYSICS, MATHEMATICAL | TRAPPED NEUTRAL ATOMS | VORTEX | EXCITED-STATES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | DILUTE GAS | defocusing/focusing nonlinearity | SEMICLASSICAL LIMIT | Physics - Mesoscale and Nanoscale Physics | Physics - Quantum Gases | Physics - Disordered Systems and Neural Networks | Physics - Other Condensed Matter | Physics - Strongly Correlated Electrons | Physics - Soft Condensed Matter | Physics - Superconductivity | Physics - Statistical Mechanics | Physics - Materials Science

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 02/2017, Volume 130, pp. 696 - 701

In this work, new exact solutions for nonlinear fractional DR equation and fractional approximate long water wave equation are obtained within the modified...

Fractional approximate long water wave equation | Fractional DR equation | (G′/G)-expansion method | Exact solution | (G '/G)-expansion method | TRAVELING-WAVE SOLUTIONS | 1ST INTEGRAL METHOD | OPTICS | International trade | Methods | Differential equations

Fractional approximate long water wave equation | Fractional DR equation | (G′/G)-expansion method | Exact solution | (G '/G)-expansion method | TRAVELING-WAVE SOLUTIONS | 1ST INTEGRAL METHOD | OPTICS | International trade | Methods | Differential equations

Journal Article